The Next 700 Program Transformers

TL;DR

This paper introduces a hierarchical framework of program transformers, extending positive supercompilation and distillation, with proven termination and analysis of potential speedups at each level.

Contribution

It defines a hierarchy of program transformers, proves their termination, and analyzes the potential speedups achievable at each level.

Findings

Transformers at each hierarchy level terminate.

Hierarchy includes positive supercompilation and distillation.

Potential speedups are characterized for each level.

Abstract

In this paper, we describe a hierarchy of program transformers in which the transformer at each level of the hierarchy builds on top of those at lower levels. The program transformer at level 1 of the hierarchy corresponds to positive supercompilation, and that at level 2 corresponds to distillation. We prove that the transformers at each level terminate. We then consider the speedups that can be obtained at each level in the hierarchy, and try to characterise the improvements that can be made.